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Frequency, also called wave frequency, is a measurement of the total number of vibrations or oscillations made within a certain amount of time. There are a few different ways to calculate frequency based on the information you have available to you. Keep reading to learn some of the most common and useful versions.

Steps

Method1

Frequency from Wavelength

1

Learn the formula. The formula for frequency, when given wavelength and the velocity of the wave, is written as: f = V / λ[1]

In this formula, f represents frequency, V represents the velocity of the wave, and λ represents the wavelength of the wave.

Example: A certain sound wave traveling in the air has a wavelength of 322 nm when the velocity of sound is 320 m/s. What is the frequency of this sound wave?

2

Convert the wavelength into meters, if necessary. If the wavelength is given in nanometers, you need to convert this value into meters by dividing it by the number of nanometers in a single meter.[2]

Note that when working with extremely small numbers or extremely large numbers, it is generally easier to write the values in scientific notation. The values will be shown in and out of their scientific notation forms for this example, but when writing your answer for homework, other schoolwork, or other formal forums, you should stick with scientific notation.

Example: λ = 322 nm

322 nm x (1 m / 10^9 nm) = 3.22 x 10^-7 m = 0.000000322 m

3

Divide the velocity by the wavelength. Divide the velocity of the wave, V, by the wavelength converted into meters, λ, in order to find the frequency, f.[3]

Example: f = V / λ = 320 / 0.000000322 = 993788819.88 = 9.94 x 10^8

4

Write your answer. After completing the previous step, you will have completed your calculation for the frequency of the wave. Write your answer in Hertz, Hz, which is the unit for frequency.

Example: The frequency of this wave is 9.94 x 10^8 Hz.

Method2

Frequency of Electromagnetic Waves in a Vacuum

1

Learn the formula. The formula for the frequency of a wave in a vacuum is almost identical to that of a wave not in a vacuum. Since there are no outside influences on the velocity of the wave, though, you would use the mathematical constant for the speed of light, which electromagnetic waves would travel at under these conditions. As such, the formula is written as: f = C / λ[4]

In this formula, f represents frequency, C represents the velocity or speed of light, and λ represents the wavelength of the wave.

Example: A particular wave of electromagnetic radiation has a wavelength of 573 nm when passing through a vacuum. What is the frequency of this electromagnetic wave?

2

Convert the wavelength into meters, if necessary. When the problem gives you the wavelength in meters, no further action is needed. If, however, the wavelength is given in micrometers, you need to convert this value into meters by dividing it by the number of micrometers in a single meter.

Note that when working with extremely small numbers or extremely large numbers, it is generally easier to write the values in scientific notation. The values will be shown in and out of their scientific notation forms for this example, but when writing your answer for homework, other schoolwork, or other formal forums, you should stick with scientific notation.

Example: λ = 573 nm

573 nm x (1 m / 10^9 nm) = 5.73 x 10^-7 m = 0.000000573

3

Divide the speed of light by the wavelength. The speed of light is a constant, so even if the problem does not provide you with a value, the value remains 3.00 x 10^8 m/s. Divide this value by the wavelength converted into meters.[5]

Example: f = C / λ = 3.00 x 10^8 / 5.73 x 10^-7 = 5.24 x 10^14

4

Write your answer. With this, you should have calculated the value of the frequency of the wave. Write your answer in Hertz, Hz, the unit for frequency.

Example: The frequency of this wave is 5.24 x 10^14 Hz.

Method3

Frequency from Time or Period

1

Learn the formula. Frequency and the time taken to finish a single wave oscillation are inversely proportional. As such, the formula for calculating frequency when given the time taken to complete a wave cycle is written as: f = 1 / T[6]

In this formula, f represents frequency and T represents the time period or amount of time required to complete a single wave oscillation.

Example A: The time for a certain wave to complete a single oscillation is 0.32 seconds. What is the frequency of this wave?

Example B: In 0.57 seconds, a certain wave can complete 15 oscillations. What is the frequency of this wave?

2

Divide the number of oscillations by the time period. Usually, you will be told how long it takes to complete a single oscillation, in which case, you would just divide the number 1 by the time period, T. If given a time period for numerous oscillations, however, you will need to divide the number of oscillations by the overall time period required to complete them.[7]

Example A: f = 1 / T = 1 / 0.32 = 3.125

Example B: f = 1 / T = 15 / 0.57 = 26.316

3

Write your answer. This calculation should tell you the frequency of the wave. Write your answer in Hertz, Hz, the unit for frequency.

Example A: The frequency of this wave is 3.125 Hz.

Example B: The frequency of this wave is 26.316 Hz.

Method4

Frequency from Angular Frequency

1

Learn the formula. When told the angular frequency of a wave but not the standard frequency of that same wave, the formula to calculate the standard frequency is written as: f = ω / (2π)[8]

In this formula, f represents the frequency of the wave and ω represents the angular frequency. As with any mathematical problem, π stands for pi, a mathematical constant.

Example: A particular wave rotates with an angular frequency of 7.17 radians per second. What is the frequency of that wave?

2

Multiply pi by two. In order to find the denominator of the equation, you need to double the value of pi, 3.14.

Example: 2 * π = 2 * 3.14 = 6.28

3

Divide the angular frequency by the double of pi. Divide the angular frequency of the wave, given in radians per second, by 6.28, the doubled value of pi.[9]

Example: f = ω / (2π) = 7.17 / (2 * 3.14) = 7.17 / 6.28 = 1.14

4

Write your answer. This final bit of calculation should indicate what the frequency of the wave is. Write your answer in Hertz, Hz, the unit for frequency.

The rate at which a vibration occurs that constitutes a wave, either in a material (as in sound waves), or in an electromagnetic field (as in radio waves and light), usually measured per second. The rate at which something occurs or is repeated over a particular period of time or in a given sample.

Use the formula c=λv. (c is the speed of light, or 2.998 x 10^8 m/s ; λ is the wavelength, or 600 nm from the given information ; and v is the frequency, the variable we are trying to find). Now it's just algebra. 2.998 x 10^8 m/s = 600 nm (v). You divide by 600 nm on both sides, of course first paying attention to units and converting 600 nm into 6 x 10^-7 m. The answer ends up being (5 x 10^14) Hz. One Hz is equal to 1/s.

To calculate the frequency of a wave, divide the velocity of the wave by the wavelength. Write your answer in Hertz, or Hz, which is the unit for frequency. If you need to calculate the frequency from the time it takes to complete a wave cycle, or T, the frequency will be the inverse of the time, or 1 divided by T. Display this answer in Hertz as well. Keep reading to learn how to calculate frequency from angular frequency!

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wikiHow is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, 24 people, some anonymous, worked to edit and improve it over time. Together, they cited 9 references. This article has also been viewed 940,307 times.